Strength and Durability of Gears

7. Strength and Durability of Gears / The tooth is the most crucial element of gears. Strength of gears depends on the breakage durability or friction durability.

Gear designers decide specifications in accordance with factors like torque, rotation and expected lifetime. In this section, we briefly introduce the bending strength and the surface durability.

Bending Strength of Spur Gears and Helical Gears JGMA401-01

As shown in the Figure.7.1, the tooth fillet breakage occurs at the root when applied force exceeds the limit. The following is the equation for bending stress :

Allowable Tangential Force (7.1)
Fig.7.1 Lack of bending stress at root
Fig. 7.1 Lack of bending stress at root

Symbol	Name	Affected Factors and other Specifications
σFlim	Allowable bending stress at rootName	Material / Heat treatment
mn	Normal Module	Tooth size
b	Face Width	Gear size
YF	Tooth Profile Factor	Pressure angle/ Profile shift coefficient / Tooth width
Yε	Load Sharing Factor	Contact ratio
Yβ	Helix Angle Factor	Helix angle of helical gear
KL	Life Factor	Expected lifetime
KFX	Size Factor of Root Stress	1.00 at the moment (unknown)
KV	Dynamic Load Factor	Circumferential speed / Gear accuracy
KO	Overload Factor	Motor / Impact from load
SF	Safety Factor	It should be set to more than 1.2 for safety considerations

How to encourage bending strength

To encourage bending strength, values in the equation for allowable tangential force (7.1) should be set to; The value of denominator should be small & The numerator should be large

Use durable materials (Increase allowable bending stress at root)
Enlarge the gear size (For large module / wide tooth width)
Strengthen tooth profile (Decrease tooth profile factor)
– Large pressure angle
– Positive correction
Increase contact ratio (Decrease load distribution factor)
– Small pressure angle
– Large tooth depth
Improve accuracy

Surface Durability of Spur and Helical Gears JGMA402-01

Tooth surface durability is calculated in accordance with the contact stress, to figure out the strength against the tooth surface damage (Pitting).

The allowable tangential force Ftlim for surface durability is;
Allowable Tangential Force Surface Durability
Allowable Tangential Force (Ftlim)

Fig.7.2 Contact Stress
Fig. 7.2 Contact Stress

Symbol	Name	Affected Factors and other Specifications
σHlim	Allowable Hertz Stress	Material / Heat treatment
d01	Pitch Diameter of Pinion	Pinion size (Diameter)
bH	Effective Facewidth	Gear size
i	Gear Ratio (z2 / z1)	Ratio of the number of teeth
ZH	Zone Factor	Helix angle / Profile shift coefficient
ZM	Material Factor	Material combination
Zε	Contact Ratio Factor	Transverse / Overlap contact ratio
Zβ	Helix Angle Factor	1.00 (Assumed)
ZHL	Life Factor	Expected lifetime
ZL	Lubricant Factor	Lubricants and Viscosity
ZR	Surface Roughness Factor	Surface roughness
ZV	Lubrication Speed Factor	Circumferential speed / Surface hardness
ZW	Hardness Ratio Factor	Hardness of wheels
KHX	Size Factor	1.00 assumed
KHβ	Longitudinal Load Distribution Factor	Gear Support / Stiffness etc.
KV	Dynamic Load Factor	Circumferential speed / Gear accuracy
K0	Overload Factor	Motor / Impact from load
SH	Safety Factor	Set to more than 1.15 for safety considerations

How to increase surface durability

Use hard material treated by quenching ( Increase allowable hertz stress )
Enlarge gear size (Large pitch diameter / Wide effective tooth width )
Increase contact ratio (Decrease contact ratio factor )
Improve accuracy

The strength calculator on KHK web site

The calculation of gear strength tends to be rather complicated. On our web site, we offer a strength calculator for KHK stock gears, which enables you to calculate gear strength automatically, by inputting values in accordance with your usage condition. For gear strength calculation, there are several formulas. The gear strength formula used in our calculator is based on JGMA (Japanese Gear Manufacturers Association) specifications.